Problem: Solve for $x$ and $y$ using substitution. ${6x+5y = 3}$ ${y = -4x-5}$
Explanation: Since $y$ has already been solved for, substitute $-4x-5$ for $y$ in the first equation. ${6x + 5}{(-4x-5)}{= 3}$ Simplify and solve for $x$ $6x-20x - 25 = 3$ $-14x-25 = 3$ $-14x-25{+25} = 3{+25}$ $-14x = 28$ $\dfrac{-14x}{{-14}} = \dfrac{28}{{-14}}$ ${x = -2}$ Now that you know ${x = -2}$ , plug it back into $\thinspace {y = -4x-5}\thinspace$ to find $y$ ${y = -4}{(-2)}{ - 5}$ $y = 8 - 5$ $y = 3$ You can also plug ${x = -2}$ into $\thinspace {6x+5y = 3}\thinspace$ and get the same answer for $y$ : ${6}{(-2)}{ + 5y = 3}$ ${y = 3}$